Trees with the greatest Wiener and edge-Wiener index

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I R Iran

Abstract

The Wiener index W and the edge-Wiener index W_e of G are defined as the sum of distances between all pairs of vertices in G and the sum of distances between all pairs of edges in G, respectively. In this paper, we identify the four trees, with the first through fourth greatest Wiener and edge-Wiener index among all trees of order n ≥ 10.